Counting plane Mumford curves

Details Counting plane Mumford curves Counting plane Mumford curves

2008-11-25

arxiv.org/abs/0811.4084v1

Physics

Mathematical Physics

13 pages, 6 figures, submitted to 5th Mathematical Physics Meeting: Summer School and Conference on Modern Mathematical Physic

Scientific paper

A $p$-adic version of Gromov-Witten invariants for counting plane curves of genus $g$ and degree $d$ through a given number of points is discussed. The multiloop version of $p$-adic string theory considered by Chekhov and others motivates us to ask how many of these curves are Mumford curves, i.e.\ uniformisable by a domain at the boundary of the Bruhat-Tits tree for $\PGL_2(\mathbb{Q}_p)$. Generally, the number of Mumford curves depends on the position of the given points in $\mathbb{P}^2$. With the help of tropical geometry we find configurations of points through which all curves of given degree and genus are Mumford curves. The article is preceded by an introduction to some concepts of $p$-adic geometry and their relation to string theory.

Affiliated with

Also associated with

No associations

Rating

Counting plane Mumford curves does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Counting plane Mumford curves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Counting plane Mumford curves will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-304482